Flexible covers can be used in combination with a variety of storage vessels, tanks, containment structures, or reservoirs that store quantities of petroleum, waste, water, etc. In some applications, such as biogas production systems, gas produced within a vessel is vented from the vessel. However, existing flexible covers can sometimes flex, dip, or bend above or below the liquid surface, trapping the gas and preventing the transmission of the gas from the vessel interior to one or more extraction openings. For example, the flow of gas out of the vessel may be inhibited if the edges of the cover are drawn, such as under negative pressure, to a position at or below a surface level of a liquid volume within the vessel. In such cases, system damage and/or system failure may result. In addition, flexible covers designed to provide insulation can be expensive and difficult to construct.